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Chemical Bonding
Lewis Theory-VSEPR Valence Bond Theory
Molecular Orbital Theory
VB theory predicts properties better than Lewis theory
bonding schemes, bond strengths, lengths, rigidity
There are still properties it doesn’t predict perfectly
magnetic behavior of certain molecules
strength of bonds
VB theory presumes the electrons are localized in orbitals
doesn’t account for delocalization
Problems with Valence Bond Theory
Molecular Orbital Theory
In MO theory, we apply Schrödinger’s wave equation to the molecule to calculate a set of molecular orbitals.
The equation solution is estimated .
We start with good guesses as to what the orbitals should look like, then test the estimate until the energy is minimized
The electrons belong to the whole molecule
orbitals are delocalized
LCAO
The simple guess starts with atomic orbitals of the atoms adding together to make molecular orbitals,
the Linear Combination of Atomic Orbitals.
The waves can combine either constructively or destructively.
Molecular Orbitals
When wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals
it is called a Bonding Molecular Orbital σ, π most of the electron density between the nuclei
Amplitudes of wave functions added
Molecular Orbitals
When wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbitals
it is called an Antibonding Molecular Orbital σ*, π* most of the electron density outside the nuclei nodes between nuclei
Amplitudes of wave functions subtracted.
Interaction of 1s Orbitals
Increasing energy
σ1s*antibonding
molecular orbital
σ1sbonding
molecular orbital
1s 1s
destructive interference
-
constructive interference
+
Molecular Orbital Theory
Electrons in bonding MOs are stabilizing.
lower energy than the atomic orbitals
Electrons in antibonding MOs are destabilizing.
higher in energy than atomic orbitals electron density located outside the internuclear axis electrons in antibonding orbitals cancel stability
gained by electrons in bonding orbitals
Molecular Orbitals and Properties
Bond Order = difference between number of electrons in bonding and antibonding orbitals
only need to consider valence electrons may be a fraction higher bond order = stronger and shorter bonds
If bond order = 0, then bond is unstable compared to individual atoms and no bond will form.
A substance will be paramagnetic if there are unpaired electrons in molecular orbitals.
A Molecular Orbital Diagram - H2
1s atomic orbital
σ
σ*
bonding MO
antibonding MO
1s atomic orbital
H· ·H
A Molecular Orbital Diagram - H2
1s atomic orbital
σ
σ*
HOMO
LUMO
1s atomic orbital
H· ·H
highest occupied molecular orbital
lowest unoccupied molecular orbital
A Molecular Orbital Diagram - H2
1s atomic orbital
σ
σ*
1s atomic orbital
H· ·H
Because more electrons are in bonding orbitals than are in antibonding orbitals,
there is a net bonding interaction.
= 1BO = ½( be – abe)
A Molecular Orbital Diagram - He2
1s atomic orbital
σ
σ*
1s atomic orbital
He: He:
Because as many electrons are in bonding orbitals as in antibonding orbitals,
NO NET BONDING INTERACTION.
= 0
X
BO = ½( be – abe)
A Molecular Orbital Diagram - Li2
2s atomic orbital
σ
σ*
2s atomic orbital
Li· ·Li
1s atomic orbital σ
σ*
1s atomic orbital
A Molecular Orbital Diagram - Li2
2s atomic orbital
σ
σ*
2s atomic orbital
Li· ·Li
Because more electrons are in bonding orbitals than are in antibonding orbitals,
there is a net bonding interaction.
= 1
2s atomic orbital
σ
σ*
2s atomic orbital
Be: :Be
MO Diagram - Be2
Because as many electrons are in bonding orbitals as in antibonding orbitals,
NO NET BONDING INTERACTION.
= 0
Interaction of p Atomic Orbitals
Each time we combine two atomic orbitals, we obtain two molecular orbitals: one bonding and one antibonding.
In the case of p atomic orbitals, overlap occurs either "head-to-head" to form σ and σ* molecular orbitals or “sideways" to form π and π*
molecular orbitals.
2pz
𝝈2p*
𝝈2p
2pz
+
Atomic orbitals
Molecular orbitals
“bonding”
“antibonding”
+
2px 2px
+
2py 2py
π2p*
+
π2p
π2p*
+
π2p
Atomic orbitals Molecular orbitals“antibonding” “bonding”
Molecular Orbitals
B2, C2, N2, O2, F2, Ne2,
2s atomic orbital
σ2s
σ2s*
2s atomic orbital
MO Diagram - B2
B B
σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
BO = ½(6 be – 4 abe) BO = 1
2s atomic orbital
σ2s
σ2s*
2s atomic orbital
MO Diagram - C2 σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
BO = ½(8 be – 4 abe) BO = 2
C C
2s atomic orbital
σ2s
σ2s*
2s atomic orbital
MO Diagram - N2 σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
BO = ½(10 be – 4 abe) BO = 3
N N
Dinitrogren ( N2 ) is Diamagnetic!!
2s atomic orbital
σ2s
σ2s*
2s atomic orbital
MO Diagram - C22-
(carbide ion) σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
BO = ½(10 be – 4 abe) BO = 3
C C
σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
Molecular Orbitals B2, C2, N2
Molecular Orbitals O2, F2, Ne2
2s atomic orbital
σ2s
σ2s*
2s atomic orbital
MO Diagram - O2 σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
BO = ½(10 be – 6 abe) BO = 2
O O
Dioxygen ( O2 ) is Paramagnetic !!
2s atomic orbital
σ2s
σ2s*
2s atomic orbital
MO Diagram - F2 σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
BO = ½(10 be – 8 abe) BO = 1
F F
2s atomic orbital
σ2s
σ2s*
2s atomic orbital
MO Diagram - Ne2 σ2p*
σ2p
π2p
π2p*
2p atomic orbital2p atomic orbital
BO = ½(10 be – 10 abe) BO = 0
Ne Ne
X
Using MO Theory to Explain Bond Properties
As the following data show, removing an electron from N2 forms an ion with a weaker, longer bond than in the parent molecules, whereas the ion formed from O2 has a stronger, shorter bond:
These facts can be explained by examining diagrams that show the sequence and occupancy of MOs.
σ2s
σ2s*
σ2p*
σ2p
π2p
π2p*
σ2s
σ2s*
σ2s
σ2s*
σ2p*
σ2p
π2p
π2p*
N2 N2+ O2 O2+
B.O.=3 B.O.=2.5 B.O.=2 B.O.=2.5
Electron is lost from bonding molecular orbital.
Electron is lost from anti- bonding molecular orbital.
σ2s
σ2s*
